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Matching Markets under (In)complete Information

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  • EHLERS, Lars
  • MASSÓ, Jordi

Abstract

We are the first to introduce incomplete information to centralized many-to-one matching markets such as those to entry-level labor markets or college admissions. This is important because in real life markets (i) any agent is uncertain about the other agents' true preferences and (ii) most entry-level matching is many-to-one (and not one-to-one). We show that for stable (matching) mechanisms there is a strong and surprising link between Nash equilibria under complete information and Bayesian Nash equilibria under incomplete information. That is,given a common belief, a strategy profile is a Bayesian Nash equilibrium under incomplete information in a stable mechanism if and only if, for any true profile in the support of the common belief, the submitted profile is a Nash equilibrium under complete information at the true profile in the direct preference revelation game induced by the stable mechanism. This result may help to explain the success of stable mechanisms in these markets.

Suggested Citation

  • EHLERS, Lars & MASSÓ, Jordi, 2007. "Matching Markets under (In)complete Information," Cahiers de recherche 01-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:01-2007
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    3. Wonki Jo Cho & Battal Doğan, 2017. "Stability and the immediate acceptance rule when school priorities are weak," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 991-1014, November.
    4. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    5. Tom Dvir & Renana Peres & Ze'ev Rudnick, 2020. "Modelling the expected probability of correct assignment under uncertainty," Papers 2008.05878, arXiv.org.
    6. Artemov, Georgy, 2021. "Assignment mechanisms: Common preferences and information acquisition," Journal of Economic Theory, Elsevier, vol. 198(C).
    7. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    8. EHLERS, Lars & MASSO, Jordi, 2018. "Robust design in monotonic matching markets: A case for firm-proposing deferred-acceptance," Cahiers de recherche 2018-02, Universite de Montreal, Departement de sciences economiques.
    9. Chen, Yi-Chun & Hu, Gaoji, 2024. "Bayesian stable states," Games and Economic Behavior, Elsevier, vol. 145(C), pages 102-116.
    10. Li, Mengling, 2020. "Ties matter: Improving efficiency in course allocation by allowing ties," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 354-384.
    11. Hoyer, B. & Stroh-Maraun, N., 2020. "Matching strategies of heterogeneous agents under incomplete information in a university clearinghouse," Games and Economic Behavior, Elsevier, vol. 121(C), pages 453-481.
    12. Britta Hoyer & Nadja Stroh-Maraun, 2017. "Matching Strategies of Heterogeneous Agents under Incomplete Information in a University Clearinghouse," Working Papers CIE 110, Paderborn University, CIE Center for International Economics.
    13. Benoit Decerf & Guillaume Haeringer & Martin Van der Linden, 2024. "Incontestable Assignments," Papers 2401.03598, arXiv.org, revised Feb 2024.
    14. Chen, Li & Sebastián Pereyra, Juan, 2019. "Self-selection in school choice," Games and Economic Behavior, Elsevier, vol. 117(C), pages 59-81.

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    More about this item

    Keywords

    Many-to-One Matching Market; Incomplete Information; Stability;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

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